Question

Integrate the function: $\frac{cos\,x}{\sqrt{4-sin^2x}}$

Answer 1

$\frac{cos\,x}{\sqrt{4-sin^2x}}$

Let sin x=t $\therefore$ cos x dx=dt

⇒∫$\frac{cos\,x}{\sqrt{4-sin^2x}}$dx=∫$\frac{dt}{\sqrt{(2)^2-(t)^2}}$

=sin-1($\frac{t}{2}$)+C

=sin-1($\frac{sin\,x}{2}$)+C